Regarding whether to leave the cover off the hive or not because part of the
bees in the swarm are on the top and sides of the box and haven't gone inside,
here is what I would do if it were me:
 
I would use my bee brush and slowly and carefully brush and "herd" as many bees
as I could into the box (at the top) then very slowly and carefully lower the
lid onto the hive box so as not to crush bees on the top but to let them get
out of the way and go down into the box.  I would leave the front entrance
open (unblocked) so the bees on the outside of the box could find the entrance
and go inside on their own.  As soon as they were settled, I would put in an
entrance feeder and restrict the entrance down (after moving the hive to the
location where I wanted to keep it).  I would keep feeding them until they got
good and established with lots of brood going, then let them continue to forage
on their own after that.  That is my opinion...someone else may have different
advice.  Good luck.
 
Layne Westover
College Station, Texas